Quantum Momentum Distributions Research Articles

Limitations of the strong field approximation in ionization of the hydrogen atom by ultrashort pulses

We present a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schr odinger equation. We show that in the impulsive limit, the Coulomb-Volkov distorted wave theory reproduces the exact solution. The validity of the strong field approximation is probed both classically and quantum mechanically. We found that classical mechanics describes the proper quantum momentum distributions of the ejected electrons right after a sudden momentum transfer, however pronounced the differences at latter stages that arise during the subsequent electron-nucleus interaction. Although the classical calculations reproduce the quantum momentum distributions, it fails to describe properly the angular momentum distributions, even in the limit of strong fields. The origin of this failure can be attributed to the difference between quantum and classical initial spatial distributions.

Atomic ionization by a sudden momentum transfer

We present a theoretical study of the distributions of ejected electrons as a result of the ionization of a hydrogen atom by a sudden momentum transfer. We show that the Coulomb–Volkov distorted wave theory in the impulsive limit reproduces the exact solution of the time dependent Schrödinger equation. The validity of the strong field approximation is also probed. We show that whereas classical and quantum momentum distributions right after a kick are identical, pronounced differences arise during the subsequent electron-nucleus interaction for weak momentum transfers.

Pulsed field ionization of Rydberg atoms

Fully quantum and classical trajectory Monte Carlo calculations are performed for a Rydberg alkali-metal atom that is kicked by a pulsed electric field. The two calculations are compared to recent experimental results through the ionization probability versus peak field strength. The energy distributions of the final electrons are compared between the two calculations. There is a qualitative difference between the classical and quantum momentum distributions which is measurable in principle. An experiment to detect the time-dependent precession of the orbital angular momentum in Cs is also proposed.

Asymptotic form of quantum momentum distributions

The behavior at large momentum, of the first density correction to the momentum distribution of a gas of interacting particles, is investigated for a wide variety of model potentials. The treatment involves neither an expansion in powers of the potential strength VO nor of Planck’s constant h/. As well, the results are valid for all temperatures and include exchange effects. It is shown that slow algebraic decay of the momentum distribution is not peculiar to hard sphere interactions, but also occurs for such smooth interactions as the Yukawa and exponential potential, whose momentum distributions decay as p−8 and p−12, respectively. The pseudopotential gives rise to a p−4 decay, in contrast to the p−6 decay for the hard sphere interaction which it is designed to model. For singular potentials of the form VO(a/r)n, a lower bound is obtained which has (almost) exponential decay.